4400 Higher June 2005 Paper 3 Q16

EdexcelHigherOld spec6 marksAdvanced Trigonometry Pythagoras

Horizontal rectangle ABCD with AB = 50 m and BC = 27 m; vertical mast AT at corner A; line TB drawn

Diagram NOT accurately drawn

\(ABCD\) is a horizontal rectangular field.
\(AB = 50\) m.
\(BC = 27\) m.
\(AT\) is a vertical mast.

(a) The angle of elevation of \(T\) from \(B\) is \(19^\circ\).
Calculate the length of \(AT\).
Give your answer correct to 3 significant figures. (3)

(b) Calculate the distance from \(C\) to \(T\).
Give your answer correct to 3 significant figures. (3)

Scheme	Marks
Angle of elevation identified	B1
\(50 \tan 19^\circ\)	M1
17.2	A1
	(3)

Mark scheme (b)

Scheme	Marks
\(50^2 + 27^2\) or 56.8(2…) or \(50^2 + \text{“}17.2\text{”}^2\) or value rounding to 52.88..	M1
\(\sqrt{\text{“}56.8\text{”}^2 + \text{“}17.2\text{”}^2}\) or \(\sqrt{\text{“}52.9\text{”}^2 + 27^2}\)	M1
59.3 – 59.4	A1
	(3)
	(6 marks)

Notes

A1: For 59.3 – 59.4